Question

For the potential-energy diagram in (Figure 1), what is the maximum speed of a 5.0 g particle that oscillates between x = 2.0 mm and x = 8.0 mm ?

Answer 1

The maximum speed of the 5.0 g particle that oscillates between x = 2.0 mm and x = 8.0 mm, is 40 m/s

How to calculate the maximum speed of the particle?

The maximum speed of the 5.0 g particle that oscillates between x = 2.0 mm and x = 8.0 mm can be calculated as illustrated below.

From the diagram given (see attached photo), the follow where obtained:

• Maximum energy = 5 J
• Minimum energy = 1 J
• Change in energy = Maximum energy - minimum energy = 5 - 1 = 4 J
• Maximum kinetic energy (KE) = Change in energy = 4 J
• Mass of particle (m) = 5 g = 5 / 1000 = 0.005 Kg
• Maximum speed (v) =?

`KE = (1)/(2)mv^2 \\\\4 = (1)/(2)\ *\ 0.005\ * v^2 \\\\4\ * 2 = 0.005\ * v^2\\\\8 = 0.005\ * v^2\\\\Divide\ both\ sides\ by\ 0.005\\\\v^2 = (8)/(0.005) \\\\v = \sqrt{(8)/(0.005)} \\\\v = 40\ m/s`

Missing part of question:

See attached photo